How entropy-theorems can show that approximating high-dim Pareto-fronts is too hard
It is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of any comparison-based multi-objective algorithm, for the Hausdorff distance, is not much better than the convergence rate of...
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Other Authors: | , , , |
Format: | Other/Unknown Material |
Language: | English |
Published: |
HAL CCSD
2006
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Subjects: | |
Online Access: | https://hal.archives-ouvertes.fr/hal-00113362/file/pareto2.pdf https://hal.archives-ouvertes.fr/hal-00113362 |
Summary: | It is empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. We here show that the convergence rate of any comparison-based multi-objective algorithm, for the Hausdorff distance, is not much better than the convergence rate of the random search, unless the number of objectives is very moderate, in a framework in which the stronger assumption is that the objectives have conflicts. Our conclusions are (i) the relevance of the number of conflicting objectives (ii) the relevance of random-search-based criterions (iii) the very-hardness of more than 3- objectives optimization (iv) some hints about new cross-over operators. |
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